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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 6762a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6762.b1 | 6762a1 | \([1, 1, 0, -564, 12384]\) | \(-3451273/9936\) | \(-57279062736\) | \([]\) | \(8064\) | \(0.75130\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6762a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 6762a do not have complex multiplication.Modular form 6762.2.a.a
sage: E.q_eigenform(10)